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A virtual pebble game to ensemble average graph rigidity

Overview of attention for article published in Algorithms for Molecular Biology, March 2015
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Title
A virtual pebble game to ensemble average graph rigidity
Published in
Algorithms for Molecular Biology, March 2015
DOI 10.1186/s13015-015-0039-3
Pubmed ID
Authors

Luis C González, Hui Wang, Dennis R Livesay, Donald J Jacobs

Abstract

The body-bar Pebble Game (PG) algorithm is commonly used to calculate network rigidity properties in proteins and polymeric materials. To account for fluctuating interactions such as hydrogen bonds, an ensemble of constraint topologies are sampled, and average network properties are obtained by averaging PG characterizations. At a simpler level of sophistication, Maxwell constraint counting (MCC) provides a rigorous lower bound for the number of internal degrees of freedom (DOF) within a body-bar network, and it is commonly employed to test if a molecular structure is globally under-constrained or over-constrained. MCC is a mean field approximation (MFA) that ignores spatial fluctuations of distance constraints by replacing the actual molecular structure by an effective medium that has distance constraints globally distributed with perfect uniform density. The Virtual Pebble Game (VPG) algorithm is a MFA that retains spatial inhomogeneity in the density of constraints on all length scales. Network fluctuations due to distance constraints that may be present or absent based on binary random dynamic variables are suppressed by replacing all possible constraint topology realizations with the probabilities that distance constraints are present. The VPG algorithm is isomorphic to the PG algorithm, where integers for counting "pebbles" placed on vertices or edges in the PG map to real numbers representing the probability to find a pebble. In the VPG, edges are assigned pebble capacities, and pebble movements become a continuous flow of probability within the network. Comparisons between the VPG and average PG results over a test set of proteins and disordered lattices demonstrate the VPG quantitatively estimates the ensemble average PG results well. The VPG performs about 20% faster than one PG, and it provides a pragmatic alternative to averaging PG rigidity characteristics over an ensemble of constraint topologies. The utility of the VPG falls in between the most accurate but slowest method of ensemble averaging over hundreds to thousands of independent PG runs, and the fastest but least accurate MCC.

Twitter Demographics

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Mendeley readers

The data shown below were compiled from readership statistics for 9 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Spain 1 11%
Unknown 8 89%

Demographic breakdown

Readers by professional status Count As %
Researcher 3 33%
Student > Master 2 22%
Student > Bachelor 1 11%
Student > Doctoral Student 1 11%
Other 1 11%
Other 0 0%
Unknown 1 11%
Readers by discipline Count As %
Computer Science 4 44%
Biochemistry, Genetics and Molecular Biology 2 22%
Sports and Recreations 1 11%
Physics and Astronomy 1 11%
Unknown 1 11%

Attention Score in Context

This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 24 April 2015.
All research outputs
#15,734,713
of 17,800,904 outputs
Outputs from Algorithms for Molecular Biology
#194
of 234 outputs
Outputs of similar age
#193,279
of 232,120 outputs
Outputs of similar age from Algorithms for Molecular Biology
#1
of 1 outputs
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